{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:30:19Z","timestamp":1760149819782,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T00:00:00Z","timestamp":1694563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12061069"],"award-info":[{"award-number":["12061069"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We obtain the separability of mixed-norm Herz-slice spaces, establish a weak convergence on mixed-norm Herz-slice spaces, and get the boundedness of the Calder\u00f3n\u2013Zygmund operator T on mixed-norm Herz-slice spaces. Moreover, we get the necessary and sufficient conditions for the boundedness of the commutator [b,T] on mixed-norm Herz-slice spaces, where b is a locally integrable function.<\/jats:p>","DOI":"10.3390\/axioms12090875","type":"journal-article","created":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T10:09:22Z","timestamp":1694686162000},"page":"875","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Necessary and Sufficient Conditions for Commutator of the Calder\u00f3n\u2013Zygmund Operator on Mixed-Norm Herz-Slice Spaces"],"prefix":"10.3390","volume":"12","author":[{"given":"Lihua","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China"}]},{"given":"Jiang","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5802\/aif.172","article-title":"Construction and analysis of some convolution algebras","volume":"14","author":"Beurling","year":"1964","journal-title":"Ann. 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